I have said this before but I say it again. I dislike cookie-cutter builds, I dislike that every character of the same class will have roughly the same attributes. I dislike this even outside the species issue, but it of course is related to that as well.
Main stats tend to be too important. One counter intuitive solution I have considered to make the main stats of each class to cost more points in point buy than other stats. So basically you could get your main stat to 16 and two secondary stats to 14, or your main stat to 14 and two secondary stats to 16. Then the optimal choice might not always be so obvious.
I also feel that classes should have better support for more variable secondary abilities. It is fine that all wizards need to be pretty smart, but there should be more leeway in assigning other attributes. Making a strong brawny wizard (who is still pretty smart) shouldn't be an idiotic choice. Subclasses could do more work here. For example there could be a some sort of Battle Wizard which fights more like a Cleric combing magic and melee.
See, you say you dislike "cookie cutter" builds, but that is exactly what Racial ASI's encourage.
Look, take two wizards, give them identical spell spellbooks. Give one a 16 INT and one a 14 INT. They are identical, except one has smaller numbers, they will miss more, their spells will be saved against more often, they have fewer spells prepared. It goes down the line.
Now take two wizards, give them identical spellbooks, and they both have an 16 INT. But one is a Dragonborn and the other is a Tabaxi. Now we have differences. The Tabaxi wizard is faster, they can get in and out of places, and they have a climb speed, they have proficiency in stealth and perception. The Dragonborn wizard has a fire breath, and resistance to fire damage (and well, that is it because dragonborn kind of suck).
The thing is though, both of those choices are mechanically inferior to picking a gnome. They are also the wizard with the 14 Int. And they are mechanically inferior to the wizard with 16 INT.
And, I know people love to post their "but I never do that" or "if you care about role-playing" stories, but the truth at my table is that I've never seen a Gnome or Halfling Fighter. Someone posted a week ago or so about DnD beyond data that showed that when talking about Humans, fighter's were more common than Paladins, but when talking about Tieflings, paladins were almost twice as likey compared to fighters.
This does have a real affect on people's choices. And if you don't like "cookie cutter builds" maybe instead of worrying if they have a +5 or a +4 to hit, you could see that making the ASI's floating means you are more likely going to see Tabaxi abilities or Aasimar abilities instead of Gnomes and Humans.
Yes, perhaps, but those characters will be pretty much the same than any other character of that class or subclass regardless of the race. Furthermore, I don't even think it is necessary for every race to be equally viable for every build. It is fine if halflings focus fighting using agility and nimbleness and orcs focus on overpowering their enemies by their physical might etc. Not everyone needs to be the same!
And the halfling wizard focuses on being worse as a wizard, because unlike fighters who can choose dex or strength, they only get INT. So, no halfling wizards.
Yes there will presumably be more race/class combinations. However, 2 things:
1. Every Barbarian will now have 16 str, 14 dex, 16 con - regardless of race. Repeat for every class. You’ve made a greater racial variation by reducing the starting stat variation. All you’ve done is trade one type of variation for another.
2. When stats considerations are removed - other features will dictate what’s best. You potentially could see fewer race/class combinations as a result of this change. That’s why I said it would presumably lead to more race/class combos - but it’s not at all a sure thing that it will.
1) Yes. That is fine. I mean, for those of you who claim that a +1 to hit doesn't matter, then why should actually getting that score matter? Every barbarian I've seen has already had a 16 Str and 16 Con, they have also all been half-orcs or goliaths. With this change, I'll see the same stats, but different races.
2) This is also fine. Combos are good. But this will make combos viable that really weren't viable before.